Mathematical analysis and numerical simulation of a model of morphogenesis
We consider a simple mathematical model of distribution of morphogens (signaling molecules responsible for the differentiation of cells and the creation of tissue patterns). The mathematical model is a particular case of the model proposed by Lander, Nie and Wan in 2006 and similar to the model pres...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2011-07-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.1035 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590210247950336 |
|---|---|
| author | Ana I. Muñoz José Ignacio Tello |
| author_facet | Ana I. Muñoz José Ignacio Tello |
| author_sort | Ana I. Muñoz |
| collection | DOAJ |
| description | We consider a simple mathematical model of distribution of morphogens (signaling molecules responsible for the differentiation of cells and the creation of tissue patterns). The mathematical model is a particular case of the model proposed by Lander, Nie and Wan in 2006 and similar to the model presented in Lander, Nie, Vargas and Wan 2005. The model consists of a system of three equations: a PDE of parabolic type with dynamical boundary conditions modelling the distribution of free morphogens and two ODEs describing the evolution of bound and free receptors. Three biological processes are taken into account: diffusion, degradation and reversible binding. We study the stationary solutions and the evolution problem. Numerical simulations show the behavior of the solution depending on the values of the parameters. |
| format | Article |
| id | doaj-art-b9cfd6955f9d40a2919171a0501a8a77 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2011-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-b9cfd6955f9d40a2919171a0501a8a772025-01-24T02:02:16ZengAIMS PressMathematical Biosciences and Engineering1551-00182011-07-01841035105910.3934/mbe.2011.8.1035Mathematical analysis and numerical simulation of a model of morphogenesisAna I. Muñoz0José Ignacio Tello1Departamento de Matemática Aplicada, ESCET, Universidad Rey Juan Carlos, 28933 Móstoles, MadridDepartamento de Matemática Aplicada, ESCET, Universidad Rey Juan Carlos, 28933 Móstoles, MadridWe consider a simple mathematical model of distribution of morphogens (signaling molecules responsible for the differentiation of cells and the creation of tissue patterns). The mathematical model is a particular case of the model proposed by Lander, Nie and Wan in 2006 and similar to the model presented in Lander, Nie, Vargas and Wan 2005. The model consists of a system of three equations: a PDE of parabolic type with dynamical boundary conditions modelling the distribution of free morphogens and two ODEs describing the evolution of bound and free receptors. Three biological processes are taken into account: diffusion, degradation and reversible binding. We study the stationary solutions and the evolution problem. Numerical simulations show the behavior of the solution depending on the values of the parameters.https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.1035steady statesexistence of solutionsreaction diffusion equationsmorphogenesisnumerical simulations. |
| spellingShingle | Ana I. Muñoz José Ignacio Tello Mathematical analysis and numerical simulation of a model of morphogenesis Mathematical Biosciences and Engineering steady states existence of solutions reaction diffusion equations morphogenesis numerical simulations. |
| title | Mathematical analysis and numerical simulation of a model of morphogenesis |
| title_full | Mathematical analysis and numerical simulation of a model of morphogenesis |
| title_fullStr | Mathematical analysis and numerical simulation of a model of morphogenesis |
| title_full_unstemmed | Mathematical analysis and numerical simulation of a model of morphogenesis |
| title_short | Mathematical analysis and numerical simulation of a model of morphogenesis |
| title_sort | mathematical analysis and numerical simulation of a model of morphogenesis |
| topic | steady states existence of solutions reaction diffusion equations morphogenesis numerical simulations. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.1035 |
| work_keys_str_mv | AT anaimunoz mathematicalanalysisandnumericalsimulationofamodelofmorphogenesis AT joseignaciotello mathematicalanalysisandnumericalsimulationofamodelofmorphogenesis |